Final answer:
The inequality that represents the relationship between the width and the perimeter of the rectangle is 2w + 2·(4w) ≤ 130, because the perimeter is at most 130 cm.
Step-by-step explanation:
The inequality that models the relationship between the width (w) and the perimeter (P) of the rectangle with length being four times its width is: 2w + 2·(4w) ≤ 130.
To find this, we formulate the perimeter of the rectangle as follows: since the length is four times the width, we express it as '4w'. The perimeter (P) of a rectangle is the sum of all its sides, which is calculated with the formula P = 2l + 2w, where l is the length and w is the width. In this case, the formula becomes P = 2·(4w) + 2w. Because the question states that the perimeter is 'at most' 130 cm, we use the 'at most' to indicate that the perimeter could be less than or equal to 130 cm, hence the ≤ symbol is appropriate for the inequality.